Energy Budget Calculations Per Lavender Flower for Foraging Honey Bees and Bumble Bees

Appendix 1

Energy budget calculations per lavender flower for foraging honey bees and bumble bees

To calculate the energy budget of a bee foragingon alavender (Lavandulaintermedia 'Grosso')flower we need to know the mean nectar energy reward perflower(Equation 1, below) and from this subtract the energy expended in nectar collection per flower,which comprises three behavioural components: flying, walking and flower handling (Equation 2, 3).Energy expenditure is usuallymeasured by the rate of either oxygen consumption or carbon dioxide production. One millilitre of oxygenused is equivalent to an energy expenditure of five calories, or 20.92 joules from carbohydrate metabolism(Heinrich 1975a).
Whilst we have a high degree of confidence in our own data on calculations of the mean energy available per flower and the duration of foraging times collected, we expect errors to exist in our energy expenditure calculations due to the inconsistencies of the values available in the literature. To counter this we haveaveraged all the appropriate data identified. Moreover, our overall conclusions are not dependent on these figures being precisely correct.
The metabolic rate of honey bee (Apismellifera) and bumble bee (Bombus spp.) flight can vary with temperature and the associated thermoregulation costs (e.g. Heinrich 1975b; RotheandNatchigall 1989), study species (e.g. Ellington et al.1990), caste (Cooper 1993 in Wolf et al. 1999), nectar load (Wolf et al.1989), reward rate (Moffatt 2001; Nieh et al. 2006), wind speed (Wolf et al. 1999) and measurement technique (Rothe 1983 in RotheandNatchigall 1989). Estimates of the metabolic rate of bumble bee free-flight at 25 C (mean temperature at study site during observations) range from 0.262 (Sivola 1984) to 0.438 J/g/s (Heinrich 1975b). Honey bee flight energetic expenditure estimates, at 20-30 C, are similar, ranging from 0.240 (RotheandNatchigall 1989) to 0.587 J/g/s (Wolf et al. 1989). Therefore, we used a mean of all available estimates; eight estimates from six studies for bumble bees (Table A) and nine estimates from eight studies for honey bees (Table A). Encouragingly, the mean values are very similar: bumble bees, 0.365 J/g/s, honey bees 0.372 J/g/s.
Data on the energy expended by walking honey bees is itself highly variable (Wolf et al.1989). We calculated a mean of 0.244 J/g/s from four measurements taken from three studies (Table 2). The only energetic estimates available for walking bumble bees (both 0.046 J/g/s) are from indolent individuals alternating between walking and resting (at 25C), Kammerand Heinrich (1974) and Sivola (1984) and so are not relevant. Therefore, we also use the A. mellifera walking mean value for Bombus as well, and justified this because the means for flying are almost identical (see above).
When calculating the metabolic rate of a bee in flight we must also consider the weight of the nectar load being carried (Wolf et al. 1989). The same is probably true for a bee walking, because for the ant Camponotusherculeanus the metabolic cost of transporting a load is the same as for additional body mass (Nielsen et al. 1982). The mean weight of A. mellifera foraging on 'Grosso' lavender is 0.097g (Balfour et al. 2013). Because, foraging A. mellifera gain c. 0.03g on a foraging trip (DukasandVisscher 1994) we estimate 0.015g (a half-load) of the weight of our honey bees (0.097g) to be nectar. But, we do not expect load weight to influence the energetics of flower handling, when a bee is on a flower and not moving its whole body. For these calculations we estimate A. melliferato weigh 0.082g (0.097 minus 0.015g) and Bombus 0.193g, mean weight of foraging B. terrestris, 0.227g (Balfour et al. 2013), minus 15%.
We could not identify any studies that measured the energy expended by A. mellifera or Bombus foragers engaged in flower handling. Therefore, we use measures of 'resting', although we expect this to be a slight underestimate. Again we use the mean of ten figures: six 'resting' and one 'grooming' estimate taken from six A. mellifera studies (Table A) and three Bombus 'resting' or 'resting/walking' estimates (Table A) in our calculations of honey bee and bumble bee flower handling energetics. Given that we expect flower handling to be more energy expensive than 'resting', we have increased this number by 25% to 0.077 J/g/s. Whether a correction of 0%, 25% or 100% was applied had no effect on our overall conclusions, Fig. 2.
Lastly, we need to consider the possible effect that flower discrimination (i.e. the acceptance or rejection of individual flowers) has on the nectar volumes collected by honey bee and bumble bees foraging on lavender. Because the accuracy of this discrimination remains unknown for our bees, we use the only appropriate estimate in the literature (Wetherwax 1986), which measured 24% more nectar in Lotus corniculatus flowers 'accepted' by honey bees than flowers sampled at random. Although this estimate is taken from another flower species, L. corniculatusand 'Grosso' lavender both have a similar proportions of empty flowers (both c. 50%) and nectar volumes (both c. 0.01- 0.02μl per flower). For our energy budget calculations we have increased the mean lavender nectar volumes (which were randomly sampled) on our patches by 24% for honey bees and by 6% for bumble bees. The bumble bee correction is 25% that of the honey bee because B. terrestris rejected approximately four times fewer lavender flower than did A. mellifera. Again, whether a correction of 10%, 25% or 50% was used had no effect on our overall conclusions, Fig. 2. Furthermore, as we found 44% of Grosso flowers without detectable nectar in our bumble bee excluded patch, we infer honey bees can access all the available nectar in a Grosso flower that it is visiting.

1. Energy reward per lavenderflower in BBE (bumble bees excluded), HBE (honey bees excluded) and CON (control) lavender patches

Assumptions
Mean nectar volume/flower from random sample: BBE:1.92× 10-5 ml, HBE:0.74× 10-5 ml, CON: 0.67× 10-5 ml (see Results)

Equation Used
The energy () of the nectar of one average lavender flower in joules(J)is the product of the mean volume (in ml) of nectar per lavender flower,the sugar concentration () of nectar lavender (39%; see Results), the specific gravity () of a solution which is 39% sugar (1.148 Brix) and the energy content of sucrose (; 16480 J/g; Kearn and Inouye 1993):

(1)

Energy per flower in each treatment patch using Equation 1

Parameter / Calculation
Energy per flower (BBE patch) / (1.92 x 10-5) × (0.39) × (1.148) × (16480) = 1.42 × 10-1 J
Energy per flower (HBE patch) / (0.74 x 10-5) × (0.39) × (1.148) × (16480) = 5.46 × 10-2 J
Energy per flower (CON patch) / (0.67 x 10-5) × (0.39) × (1.148) × (16480) = 4.94 × 10-2 J

Increased energy per flower on lavender patches due to bee discrimination among flowers

Honey bees (+24%):BBE: 1.76× 10-1J, CON: 6.13 × 10-2J
Bumble bees (+6%): HBE: 5.79 ×10-2J, CON: 5.24 × 10-2J

2. Energy expenditure per lavender flowerfor honey bees (Apismellifera)

Assumptions

Metabolic rate of 'flying' honey bee = 0.372J/g/s(mean of 9A. melliferavalues)
Metabolic rate of'walking' honey bee = 0.244 J/g/s (mean of 4A. melliferavalues)
Metabolic rate of 'flower handling' honey bee= 0.077 J/g/s (mean of 7A. mellifera/Bombusvalues)
Mean weight of honey bees foraging on 'Grosso' lavender = 0.097g (Balfour et al. 2013)

Time spent in different foraging activities per lavender flower (this study, Table A)

Equations Used

The mean energy expended () by a bee per probed lavender flower is the sum of the energy expended in all foraging activities: flying (), walking () and flower handling ():

(2)

Energy (in Joules, J) expended per activity ( and ) is the product of the metabolic rate () of activity in J/g/s, the mean bee weight (, in grams, g) and the mean time () spend engaged in this activity per lavender flower, e.g.:

(3)

The energy expended per flower by A. mellifera on Bumble bee excluded (BBE) patch, using Equation 2 & 3

Honey bee energy/flower (flying) / (0.372) × (0.097) × (0.407) = 1.47 × 10-2 J
Honey bee energy/flower (walking) / (0.244) × (0.097) × (0.663) = 1.57 × 10-2 J
Honey bee energy/flower (handling) / (0.077) × (0.082) × (2.130) = 1.34 × 10-2 J
Total / (1.47 × 10-2) + (1.57 × 10-2) + (1.34 × 10-2) = 4.38 × 10-2 J

The energy expended per flower by A. mellifera on Control patch (CON) patch, using Equation 2 & 3

Honey bee energy/flower (flying) / (0.372) × (0.097) × (0.947) = 3.42 × 10-2 J
Honey bee energy/flower (walking) / (0.244) × (0.097) × (0.533) = 1.26 × 10-2 J
Honey bee energy/flower (handling) / (0.077) × (0.082) × (1.890) = 1.19 × 10-2 J
Total / (3.42 × 10-2) + (1.26 × 10-2) + (1.19 × 10-2) =5.87 × 10-2 J

3. Energy expenditure per lavender flower for bumble bees (Bombusterrestris)

Assumptions
Metabolic rate of a 'flying' bumble bee = 0.365J/g/s(mean of 8Bombusvalues)
Metabolic rate of 'walking' bumble bee = 0.244 J/g/s (mean of 4A. melliferavalues)
Metabolic rate of 'flower handling' bumble bee = 0.077 J/g/s (mean of 7 A. mellifera/Bombusvalues)
Mean weight of bumble bees foraging on 'Grosso' lavender = 0.227g [16]
Time spent in different foraging activities per lavender flower (this study, Table A)

Bumble bee energy/flower (flying) / (0.365) × (0.227) × (0.054)= 0.45 × 10-2 J
Bumble bee energy/flower (walking) / (0.244) × (0.227) × (0.286)= 1.58 × 10-2 J
Bumble bee energy/flower (handling) / (0.077) × (0.193) × (0.810) = 1.20 × 10-2 J
Total / (0.45 × 10-2)+ (1.58 × 10-2) + (1.20 × 10-2)= 3.23 × 10-2 J

The energy expended per flower by B. terrestris on Honey bee excluded (HBE) patchusing Equations 2 and 3

The energy expended per flower by B. terrestris on Control(CON) patchusing Equations 2 and 3

Bumble bee energy/flower (flying) / (0.365) × (0.227) × (0.067)= 0.56 × 10-2 J
Bumble bee energy/flower (walking) / (0.244) × (0.227) × (0.284)= 1.57 × 10-2 J
Bumble bee energy/flower (handling) / (0.077) × (0.193) × (0.770) = 1.14 × 10-2 J
Total / (0.56 × 10-2)+ (1.57 × 10-2) + (1.14 × 10-2)= 3.27 × 10-2 J

References

Balfour NJ,Garbuzov M, Ratnieks FLW (2013) Longer tongues and swifter handling: why do more bumble bees (Bombus spp.) than honey bees (Apismellifera) forage on lavender (Lavandula spp.)? Ecol Entomology38:323-329

Bertsch A (1984) Foraging in male bumblebees (Bombuslucorum L.): maximizing energy or minimizing water load? Oecologia 62:325-336

Dukas R, Visscher PK (1994) Lifetime learning by foraging honey bees. AnimBehav48:1007-1012

Ellington CP, Machin KE, Casey TM (1990) Oxygen consumption of bumblebees in forward flight. Nature 347:472-473

Goller F, Esch HE (1991) Oxygen consumption and flight muscle activity during heating in workers and drones of Apismellifera. JComp Physiology B 161:61-67

Harrison JF, Fewell JH (2002) Environmental and genetic influences on flight metabolic rate in the honey bee, Apismellifera. Comp BiochemPhysiol A 133:323-333

Heinrich B (1975a) Energetics of pollination. Annual Rev Ecol System 6:139-170

Heinrich, B. (1975b) Thermoregulation in bumblebees II. Energetics of warm-up and free flight. J Comp Physiology B 96:155-166

Joos B, Lighton JR, Harrison JF, Suarez RK, Roberts SP (1997) Effects of ambient oxygen tension on flight performance, metabolism, and water loss of the honeybee. PhysiolZoology70:167-174

Kammer AE, Heinrich B (1974) Metabolic rates related to muscle activity in bumblebees. J ExperBiol 61:219-227

Kearns CA,Inouye DW (1993) Techniques for pollination biologists. University Press of Colorado, Boulder

Moffatt L (2001) Metabolic rate and thermal stability during honeybee foraging at different reward rates. J ExperBiol204:759-766

Nieh JC, León A, Cameron S, Vandame R (2006) Hot bumble bees at good food: thoracic temperature of feeding Bombuswilmattae foragers is tuned to sugar concentration. J ExperBiol209:4185-4192

Nielsen MG, Jensen TF, Holm-Jensen I B (1982) Effect of load carriage on the respiratory metabolism of running worker ants of Camponotusherculeanus (Formicidae). Oikos, 39:137-142

Rothe U, Nachtigall W (1989) Flight of the honey bee. J Comp Physiology B 158:739-749

Silvola J (1984) Respiration and energetics of the bumblebee Bombusterrestrisqueen. Ecography7:177-181

Stabentheiner A, Vollmann J, Kovac H, Crailsheim K (2003) Oxygen consumption and body temperature of active and resting honeybees. J Insect Physiol 49:881-889

Wetherwax PB (1986) Why do honeybees reject certain flowers? Oecologia 69:567-570

Wolf TJ, Schmid-Hempel P, EllingtonCP, Stevenson RD (1989) Physiological correlates of foraging efforts in honey-bees: oxygen consumption and nectar load. Funct Ecol 3:417-424

Wolf TJ, Ellington CP, Begley IS (1999) Foraging costs in bumblebees: field conditions cause large individual differences. InsectesSociaux 46:291-295

Table A1. Bee respiration rates (O2 consumption or CO2 production) used to calculate the energy expended by honey bees (Apismellifera) and bumble bees (Bombus sp.) whilst flying, walking and flower handling.† in Wolfe, Ellington and Begley 1999;*in Wolf et al. 1989; ** in Rothe and Natchigall 1989

Study / Study Species / Caste / Activity / J/g/s
Hocking 1953 / A. mellifera / Workers / Flying tethered on roundabout / 0.351
Sotavalta 1954 / A. mellifera / Workers / Flying tethered on roundabout / 0.311
Scholze et al. 1983 / A. mellifera / Workers / Flying to feeding dish / 0.475
Rothe 1983* / A. mellifera / Workers / Flying tethered on roundabout / 0.360
Rothe 1983* / A. mellifera / Workers / Flying in wind tunnel / 0.300
Wolf et al. 1989 / A. mellifera / Workers / Flying in wind tunnel / 0.546
Rothe and Nachtigall 1989 / A. mellifera / Workers / Flying in wind tunnel / 0.240
Joos et al. 1997 / A. mellifera / Workers / Flying in respirometry chamber / 0.340
Harrison and Fewell 2002 / A. mellifera / Workers / Flying in respirometry chamber / 0.429
Heinrich 1975b / B. edwardsii / Queens / Flying / 0.448
Heinrich 1975b / B. vosnesenskii / Queens / Flying / 0.372
Bertsch 1984 / B. locurum / Drones / Flying / 0.436
Sivola1984 / B. terrestris / Queens / Flying / 0.244
Ellington et al. 1990 / B. locorum / Workers / Flying / 0.348
Ellington et al 1990 / B. pascuorum / Workers / Flying / 0.305
Cooper 1993† / B. locurum / Workers / Flying / 0.325
Wolfe, Ellington and Begley 1999 / B. terrestris / Workers / Flying in greenhouse / 0.445
Rothe and Natchtigall 1989 / A. mellifera / Workers / Walking on polystyrene ball / 0.167
Wolf et al. 1989 / A. mellifera / Workers / Walking / 0.247
Stabentheiner et al 2003 / A. mellifera / Workers / Walking slowly / 0.262
Stabentheiner et al 2003 / A. mellifera / Workers / Walking fast/ready to fly / 0.298
Hocking 1953 / A. mellifera / Workers / Resting / 0.018
Cahill andLustick 1976 / A. mellifera / Workers / Resting / 0.117
Withers 1981** / A. mellifera / Workers / Resting / 0.071
Rothe and Natchigall 1989 / A. mellifera / Workers / Resting / 0.006
Goller and Esch 1991 / A. mellifera / Workers / Resting / 0.016
Stabentheheiner et al. 2003 / A. mellifera / Workers / Grooming/resting/little steps / 0.167
Stabentheheiner et al. 2003 / A. mellifera / Workers / Resting / 0.013
Kammer and Heindrich 1974 / B. vosnesenskii / Queens/workers / Resting / 0.046
Bertsch 1984 / B. lucorum / Drones / Resting / 0.116
Sivola 1984 / B. terrestris / Queens / Resting/walking / 0.046

Appendix 2

Figure A1

Fig. A1. Predicted response (stay or leave) of bumble bees (Bombus spp.) and honey bees (A. mellifera) to nectar amounts per flower. The numbers on the horizontal axis are taken from the mean nectar volume per flower in our control (0.007μl) and bumble bee excluded patches (0.019μl), see Results. The bumble bee curve is to the left of the honey bees curve because Bombus can make a profit at 0.007μl and visit flowers 3 times more quickly than honey bees (Balfour et al. 2013). Figure based on Fig. B2.3 in Stephens DW, Krebs JR (1986) Foraging theory. Princeton University Press, Princeton.